Question

In an ellipse, the ratio of the distance between the foci and the length of the major axis is called:

Answer 1

The ratio of the distance between the foci and the length of the major axis is called eccentricity.

Definitions of dimensions in ellipses

Dimensionally speaking, an ellipse is characterized by three variables:

1. Length of the major semiaxis ($a$).
2. Length of the minor semiaxis ($b$).
3. Distance between the foci and the center of the ellipse ($c$).

And there is the following relationship:

$c = \sqrt{a^{2}-b^{2}}$ (1)

Another variable that measure how "similar" is an ellipse to a circle is the eccentricity ($e$), which is defined by the following formula:

$e = \frac{c}{a}$, $0 \ge c \ge 1$ (2)

The greater the eccentricity, the more similar the ellipse to a circle.

Therefore, the ratio of the distance between the foci and the length of the major axis is called eccentricity. $\blacksquare$

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